Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14555768 | C2 | semidirect |
| 2. #22581460 | C2 | semidirect |
| 3. #22581208 | C2 | semidirect |
| 4. #22581203 | C2 | semidirect |
| 5. #22581196 | C2 | semidirect |
| 6. #22580991 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. C2×#135×C139 | C2 | semidirect |
| 20. #17984776 | C22 | semidirect |
| 21. #17984774 | C22 | semidirect |
| 22. #17984766 | C22 | semidirect |
| 23. #17984763 | C22 | semidirect |
| 26. C2×Q16×C139 | C22 | semidirect |
| 27. C2×SD16×C139 | C22 | semidirect |
| 28. C2×D8×C139 | C22 | semidirect |
| 57. C2×C8×C139 | D4 | semidirect |
| 105. C139 | #3054 | semidirect |
| 107. C2×#135 | D139 | semidirect |
| 118. C2×Q16 | C2×D139 | semidirect |
| 119. C2×SD16 | C2×D139 | semidirect |
| 120. C2×D8 | C2×D139 | semidirect |
| 157. C2×C8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555768 | 2 |
| #22581460 | 2 |
| #22581208 | 2 |
| #22581203 | 2 |
| #22581196 | 2 |
| #22580991 | 2 |
| #22580949 | 2 |
| C2×#135×C139 | 2 |
| #3054 | 139 |